After a query has produced an output table (after the select
list has been processed) it can optionally be sorted. If sorting
is not chosen, the rows will be returned in an unspecified order.
The actual order in that case will depend on the scan and join
plan types and the order on disk, but it must not be relied on. A
particular output ordering can only be guaranteed if the sort
step is explicitly chosen.

The sort expression(s) can be any expression that would be
valid in the query's select list. An example is:

SELECT a, b FROM table1 ORDER BY a + b, c;

When more than one expression is specified, the later values
are used to sort rows that are equal according to the earlier
values. Each expression can be followed by an optional ASC or DESC keyword to
set the sort direction to ascending or descending. ASC order is the default. Ascending order puts
smaller values first, where "smaller"
is defined in terms of the <
operator. Similarly, descending order is determined with the
> operator. [1]

The NULLS FIRST and NULLS LAST options can be used to determine
whether nulls appear before or after non-null values in the sort
ordering. By default, null values sort as if larger than any
non-null value; that is, NULLS FIRST is
the default for DESC order, and
NULLS LAST otherwise.

Note that the ordering options are considered independently
for each sort column. For example ORDER BY x,
y DESC means ORDER BY x ASC, y
DESC, which is not the same as ORDER BY
x DESC, y DESC.

For backwards compatibility with the SQL92 version of the
standard, a sort_expression can
instead be the name or number of an output column, as in:

SELECT a + b AS sum, c FROM table1 ORDER BY sum;
SELECT a, max(b) FROM table1 GROUP BY a ORDER BY 1;

both of which sort by the first output column. Note that an
output column name has to stand alone, it's not allowed as part
of an expression — for example, this is not correct:

SELECT a + b AS sum, c FROM table1 ORDER BY sum + c; -- wrong

This restriction is made to reduce ambiguity. There is still
ambiguity if an ORDER BY item is a
simple name that could match either an output column name or a
column from the table expression. The output column is used in
such cases. This would only cause confusion if you use AS to rename an output column to match some other
table column's name.

ORDER BY can be applied to the result
of a UNION, INTERSECT, or EXCEPT
combination, but in this case it is only permitted to sort by
output column names or numbers, not by expressions.

Notes

Actually, PostgreSQL uses
the default B-tree operator class
for the expression's data type to determine the sort ordering
for ASC and DESC. Conventionally, data types will be set
up so that the < and > operators correspond to this sort
ordering, but a user-defined data type's designer could
choose to do something different.